Ferroelectrics. Disordered Ferroelectrics · DC) Ferroelectricity: Polarization reversible. (P-E...

Ferroelectrics. Disordered Ferroelectrics

1Physics 403 Summer 2020

• Ferroelctricity

• Main properties

•History. Discovery. Materials

• Disordered Ferroelectrics Relaxors

• Applications


• Ferroelectric Materials. A ferroelectric material

is a material that exhibits, over some range of

temperature, a spontaneous electric

polarization that can be reversed or reoriented

by application of an electric field.

3

An American National StandardIEEE Standard Definitions ofPrimary Ferroelectric Terms

Physics 403 Summer 2020

Ferroelectricity: Two classes of ferroelectrics

Displacement type

N

O

O

Order-Disorder

disorder

order

NaNO2

Ba

Ti O

P

PBaTiO3


-40 -30 -20 -10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40 Sn:Ti = 0.24:0.11

PLZST ceramics

P (C

/cm

2)

EDC

(kV/cm)

Ferroelectricity: Polarization reversible. (P-E hysteresis)


Ferroelectricity: Domains

+

-

Pnet~0

Single domain state

Multi domain state

180o domain pattern

90o domains

Y Lu et al. Science 1997;276:2004-2006

Courtesy of Igor Lukyanchuk

http://www.lukyanc.net/stories/nano-worldofdomains


Ferroelectricity: Domains

Courtesy of Benjamin Vega-Westhoff

and Scott Scharfenberg, P403, Fall2009

BaTiO3

BaTiO3

Crystal from Forschungsinstitutfür mineralische und metallische

Werkstoffe -Edelsteine/Edelmetalle

KH2PO4

Courtesy of Allison Pohl, P403,

Fall2009

KD2PO4191K

PMN-PT40%

PMN-PT30%


Ferroelectricity: Landau-Ginzburgphenomenological theory

EPcPbPaPFP −+++= ...6

1

4

1

2

1 642

Free energyOrder parameter (polarization)

Electric fieldthe equilibrium solution 0=

P

F

Ignoring higher terms we can get the linear solution:

0F

aP EP

= − =

aE

P 1=

=

Assuming linear dependence of a on temperature we will have:

1( )

cT T

C = − and finally we will have Curie-Weiss law

( )c

C

T T =

−

Lev Landau1908-1968

Vitaly Ginzburg1916-2009


-7 0 7

0

10

20

30

40

50

60

70

80

F (

a.u

.)

P (a.u.)


In case of b>) (C>0 also) We will

have the solution for second

order phase transition with two

equilibrium points –p0 and p0.

Both these states are equivalent

T>Tc

T=Tc

T<Tc

E=0

p0-p0


-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-40 -30 -20 -10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40 Sn:Ti = 0.24:0.11

PLZST ceramics

P (C

/cm

2)

EDC

(kV/cm)


EPcPbPaPFP −+++= ...6

1

4

1

2

1 642

Including EP term can illustrate

the P-E hysteretic behavior

-PsPs

Pr

Pr

Ps


400 450 5000

3

6

9

T (K)

'/1

00

0Ferroelectricity: Susceptibility

0P E = 0 0 0 0 0

(1 )D E P E E E E = + = + = + =

For ferroelectrics >>1 and ≈

Curie-Weiss law:

00)(

+−

=CWTT

C

C=1.9*105;

TC=385.2K

BaTiO3


Rochelle Salt KNaC4H4O6*4H2O

Potassium sodium tartrate discovered (in about 1675) by an apothecary, Pierre Seignette

Elie Seignette

Rochelle Salt originates fromFrench city of La Rochellewhere it was produced byPierre Seignette anothername of this material isSeignette salt

Rochelle Salt was used

in medicine and food

industry



Paul-Jacques Curie1856 – 1941

Pierre Curie1859-1906

Brothers Curie discovered and investigated the piezoelectric effect I several materials including Rochelle salt



Joseph Valasek (1897-1993)

University of Minnesota

1920 1969

1. J. Valasek, Phys. Rev. 17, 475 (1921)

2. J. Valasek, Phys. Rev. 19, 478 (1922)

Fig.1. The first published

hysteresis loop [1]Fig3. Piezoelectric

response as a function

of temperature [2]


Ferroelectricity. Terminology.

ferrum (Lat) gave the name of the broad class of magnetic materials – ferromagnetics

Fe has no relation to the phenomenon of ferroelctricity but

because of a lot of common features of ferroelectric phase transition to ferromagnetic the “new” class of dielectrics was named as ferroelectrics.

There is another name for this class of materials - Seignette-electrics named after the alternative name of the Rochelle salt


16

KDP (KH2PO4) - potassium dihidrophosphate

G. Busch and P. Scherrer, Naturwiss. 23, 737 (1935). Eine neue Seignetteelektrische Substanz. 1935

Paul Scherrer1890-1969

Georg Busch 1908-2000

Tc ~123K


17

KDP (KH2PO4) - potassium dihidrophosphate Tc ~121-123 K

100 150 200 2500

1

2

31000kHz

KDP (sample 4) c-cutheating

T (K)

'/1

00

0

KDP project (2): Graph6

Courtesy of Tim S. Thorp, Zhangji Zhao, Physics 403, Spring 2013

Tc~121.5 K

Courtesy of Alison Pohl, Physics 403, Spring 2009

T>Tc

T<Tc


18

DKDP (KD2PO4) – deuterated potassium dihidrophosphateTc ~230K

T>Tc

T<Tc


19

1943 – material with high (>1200) value of the dielectric constant (Wainer, Solomon (USA); Wul, Goldman (USSR))

Tc ~400K

1945 – discovered the ferroelectric properties of BaTiO3 A. von Hippel (USA); Wul, Goldman (USSR))

Arthur R. von Hippel1898-2003

A. Von Hippel, Rev. Mod. Phys. 22,221, 1950Physics 403 Summer 2020

20

tetragonal

orthorhombic

rhombohedral

Walter J. Merz, Phys. Rev. 76, 1221, 1949

’P

(

C/c

m2)

P

P

P


21

John A. Hooton, Walter J. Merz, Phys. Rev. 98, 409,1955

Physics 403 Lab, August 2011


22

150 200 250 300 350 400 450 5000

3

6

9

cooling

heating

100Hz

T (K)

'/1

000

-20 -15 -10 -5 0 5 10 15 20

-30

-20

-10

0

10

20

30

345K

395K

P (

C/c

m2)

E (kV/cm)

395K345K

Courtesy of Liu M. & Lopez P, Physics 403, Spring 2013


Ferroelectricity: Typical ferroelectric materials

Number of publications concerning ferroelectricity. From

Jan Fousek “Joseph Valasek and the Discovery of

Ferroelectricity”

Springer Handbook of Condensed Matter and Materials Data

TC(K) Ps (C/cm2)

KDP

type KH2PO4 123 4.75

KD2PO4 213 4.83

RbH2PO4 147 5.6

Perovskites BaTiO3 408 26

KNbO3 708 30

PbTiO3 765 >50

LiTiO3 938 50

LiNbO3 1480 71

ABO3


Perovskite Structure

AB1(1-x)B2xO3 A1(1-x)A2xBO3 A1(1-x)A2xB1(1-y)B2yO3 typical complex oxides with perovskite structure

Perovskite is a mineral CaTiO3. The mineral was discovered in the Ural Mountains

of Russia by Gustav Rose in 1839 and is named after Russian mineralogist Lev

Perovski.

Gustav Rose1798-1873

Lev Perovski1792-1856


New Perovskite Materials - Relaxors

Smolenskii G.A.2

(1910 – 1986)L. Eric Cross1

(1923-2016)

B-site complex

Lead magnesium niobate(PMN)

PbMgl/3Nb2/303

Lead scandium tantalate(PST)

PbSc1/2Ta1/203

Lead zinc niobate (PZN) PbZnl/2Nb1/203

Lead indium niobate (PIN) PbIn1/2Nb1/203

A-site complex

Lead lanthanum titanate(PLT)

Pb1-xLaxTiO3

Both sites complex

Lead lanthanum zirconate titanate (PLZT)

Pb1−xLaxZryTi1−yO3

Potassium lead zinc niobate K1/3Pb2/3Zn2/9Nb7/903 1. Pennsylvania State University, USA2. A.F. Ioffe Institute, USSR

AB1(1-x)B2xO3 A1(1-x)A2xBO3 A1(1-x)A2xB1(1-y)B2yO3 typical complex oxides with perovskite structure


Relaxors

Ba O Ti

Relaxor - PMN Pb(Mg1/3 Nb2/3)O3Regular ferroelectric BaTiO3

OPb Mg+2 or Nb+5

T > Tc (cubic) (cubic)


Relaxors

Ba O Ti

Relaxor - PMN Pb(Mg1/3 Nb2/3)O3Regular ferroelectric BaTiO3

OPb Mg+2 or Nb+5

T < Tc (tetragonal) (cubic)


Temperature dependencies of ’ measured in a

broad frequency range: 3mHz -1MHz

150 200 250 300 350 400 4500

7

14

21

28

35

T (K)

'/1

000

0.05

0.10

0.15

0.20

0.25

0.30

0.35

10

3/

'

3mHz

1MHz

’max and Tmax depend on the measuring frequency

’ does not follow Curie-Weiss law


250 255 260 265 270 275 280 285 29010

-3

10-1

101

103

105

TVF

~212K

f ma

x (

Hz)

Tmax

(K)

0

max 0exp

VF

Ef f

T T

−=

−


Figure 3.(a) ABO3perovskite structure. (b) Model for relaxor structure. PNR and COR represent the polar nano-region and chemically order region, respectively. (c) &(d) show two models of atom arrangement for COR. To maintain the electric neutrality, a Nb-rich layer is required for case (c).

PNR – polar nanodomainsCOR – chemically ordered regions

D. Fu, et all in "Advances in Ferroelectrics", ISBN 978-953-51-0885-6, November 19, 201230Physics 403 Summer 2020

100 200 300 400

0

5000

10000

15000

20000

25000

30000

'

T (K)

Regular Ferroelectrics - Relaxors

PMN BaTiO3

31Physics 403 Summer 2020BTO courtesy of James Graessle

Same structure but different behavior

Disorder in Regular Ferroelectrics

BaTiO3 Rhombohedral phase


150 200 250 300 350 400

5

10

15

20

25

'/1

00

0

100 Hz

20 kHz

100 120 140 160 180 200 2200.5

1.0

1.5

2.0

2.5

3.0

3.5

'/1

000

T (K)

100Hz

20 kHz

BTO courtesy of James Graessle

(111)E

PMN remains in cubic phasebut it is easy to move it inrhombohedral phase byapplication of the DC field in(111) direction

PMN

BaTiO3

Disorder in Regular Ferroelectrics. KDP family


KH2PO4

KD2PO4

KDP - Tc ~ 120 K

Deuterated analog DKDP Tc~230K

80 100 120 140 160 180 2000

500

1000

T (K)

'

500m 1 20.0

0.5

1.0

KDP

BTO

T/Tc

'/

' ma

x BaTiO3

KH2PO4



80 90 100 110 120 130 140 1500.0

0.5

1.0

T (K)

'/1

00

0

100 Hz

50 kHz

120 140 160 180 200 220 240 2600.0

0.5

1.0

T (K)

'/1

00

0

100 Hz

20 kHz

KD2PO4KH2PO4

Below Tc KDP and DKDP show wide (> 30 K)

plateau. This state is not equilibrium and has a

trend to decrease the susceptibility in time (aging)



Aging depends on the concentration of deuterium

in (KH2PO4)(1-x)(KD2PO4)x composition

200 220 240 260 280 300

400

600

800

1000

1200

'

T (K)

cooling

aging

KD2PO4

0 50 100 150 200 250 300

400

500

600

700

800

900

1000

time (h)

'

T=200 K

~ 270 hours of aging



Aging does not significantly change the domain

pattern of the KDP-DKDP ferroelectric. The

rearrangements in domain walls are responsible for

the decrease of the susceptibility.

t = 0 t = 10 h



Finally, at low T these nanoscale polarized regions

becomes frozen and do not more contribute low

field susceptibility.

100 120 140 160 180 2000.0

0.2

0.4

0.6

0.8

100Hz

T (K)

'/1

00

0

155 160 165 170 175

20

40

60

80 100 Hz

500 Hz

1 kHz

2 KHz

5 KHz

10 kHz

20 kHz

T (K)

''

Tmax

165.0 165.5 166.0 166.5 167.04

6

8

10

ln(f

)

Tmax (K)

0

max

exp a

VF

Ef f

T T

−=

−

TVF=163.5 KPMN

DKDP

Physics 403 Summer 2020 38

Applications of Ferroelectrics

KDP single crystals are mostly used as nonlinear optical materials

KDP powder is widely used as fertilizer

0.0 0.1 0.2 0.3 0.4 0.5

300

400

500 Literature data

single crystals

ceramicsT

c (K

)

x

(PMN)(1-x)(PT)(x)

phase diagram

“Relaxor”

Ferroelectric

Paraelectric

(cubic)

(PMN)0.9(PT)0.1(PMN)0.7(PT)0.3

(PMN)0.6(PT)0.4

(PMN)0.97(PT)0.03

PT: PbTiO3, ferroelectric with

Curie temperature 763K

Solid solution relaxor-regular ferroelectric.


Courtesy of D. Tenne, Boise State University40Physics 403 Summer 2020

Courtesy of D. Tenne, Boise State University41Physics 403 Summer 2020

Applications of Ferroelectrics. Physics 403 Lab

AFM experimentQuantum Optics

Applications. Nonvolatile Memory

Fast write speed (65-70ns)High endurance (1014 cycles)Low power consumption


Applications. Actuators

Piezo-injector for diesel engines, (b) Multilayer piezoelectric actuator scheme.

(a)

(b)

Courtesy Technische Universität Darmstadt

Atomic Force Microscope

Lead Zirconium Titanate piezo scanner

PI (www.pi.ws)


Applications. SonarsMilitary Applications

44

APPLICATIONS:

MINE HUNTINGWEAPONS SONARCOUTERMEASURESACOUSTIC COMMUNICATIONSPROJECTOR ARRAYSHYDROPHONE ARRAYSVIBRATION CONTROL

Piezocomposite materials have been testedby the United States military since 1992.


Applications. SonarsCivil Applications

45

Courtesy

Fish Finder


46

Applications. Adaptive Optics

Reflecting surface

Soldered control and mass wires

Courtesy of

http://scmero.ulb.ac.be

PZT – Lead Zirconium Titanate Pb[ZrxTi1-x]O3


47

Material Dielectric

constant

Piezoelectric

coefficient, (pC/n)

Electromechanical

coupling factorQuartz 4.5 2.3 0.1

Rochelle salt (30C) 9.2 27 0.3

Barium titanate

ceramic

1700 190 0.52

Lead zirconate

titanate PZT 45/55

450 140 060

PMN-PT (sc) 4200 2200 0.92-0.94

PZN-PT (sc) 2500 2400 0.91-0.93

Actuators TransducersAdaptive opticsCapacitorsLine motors for SFM

Transducer stack for

ultrasonic sonar application

(TRS Ceramics)

Piezoelectric

properties of different

materials

Ferroelectricity: Relaxors - aplications


Ferroelectrics. Disordered Ferroelectrics · DC) Ferroelectricity: Polarization reversible. (P-E...

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